Asynchronously switched control of a class of slowly switched linear systems

The stabilization problem for a class of switched linear systems with average dwell time (ADT) switching is reinvestigated in this paper. State-feedback controllers are designed, which takes the more practical case, asynchronous switching, into account, where the so-called “asynchronous switching” indicates that the switchings between the controllers and the system modes are in the presence of a time delay. By combining the asynchronous switching, an improved stabilization approach is given, and existence conditions of the controllers associated with the corresponding ADT switching are formulated in terms of a set of linear matrix inequalities. A numerical example is given to show the validity and potential of the obtained theoretical results.